Finite Group Databasebeta

← #14322017

Subgroups — #14322017

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91455C211yesmaximal, characteristic
2C2×#91444C211yesmaximal, characteristic
3C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
4#11750771C211yesmaximal, characteristic, complemented
5C5×#4646C211yesmaximal, characteristic, complemented
6C3×#64955C211yesmaximal, characteristic, complemented
7#11748912C211yesmaximal, characteristic
8#11748875C211yesmaximal, characteristic, complemented
9#11748875C211yesmaximal, characteristic, complemented
10#11748772C211yesmaximal, characteristic, complemented
11#11748710C211yesmaximal, characteristic, complemented
12#11748702C211yesmaximal, characteristic, complemented
13#11748668C211yesmaximal, characteristic, complemented
14#11748652C211yesmaximal, characteristic, complemented
15C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
16#10608211—31nomaximal, Hall
17C22×C5×Dic6C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×#1202C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×Dic3⋊Dic5C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×#6667C2211yescharacteristic
36C2×#6665C2211yescharacteristic
37C2×#6665C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44#91455C418yescomplemented
45#91444—24no—
46Dic5×Dic6—24no—
47C3×C5×#95C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C5×C3⋊#95C2211yescharacteristic
51C5×C3⋊#95C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55C4×#885—51nomaximal, Hall
56C2×#4093—31no—
57C2×Q8×Dic5—31no—
58C2×#4039—31no—
59C5×#391—31no—
60#65266—31no—
61#65228—31no—
62C42×Dic5—31no—
63#64959—31no—
64#64959—31no—
65#64959—31no—
66#64959—31no—
67#64955—31no—
68#64955—31no—
69#64955—31no—
70#64955D311yescharacteristic, complemented
71C23×D15C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C2×C5×Dic6—22no—
84C2×C5×Dic6—22no—
85C2×C5×Dic6C2×C414yescomplemented
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×C3×C4×D5—22no—
90C2×C3×C4×D5—22no—
91C2×C3×C4×D5—22no—
92C2×#1202—22no—
93C2×#1202—22no—
94C2×#1202C2×C414yes—
95C2×#1200—22no—
96C2×#1200—22no—
97C2×#1200—22no—
98#6714—22no—
99#6714—22no—
100#6714C2×C414yescomplemented
101C4⋊Dic15—22no—
102C4×Dic15—22no—
103C5×Dic3⋊C4—22no—
104C4×C5×Dic3—22no—
105C3×#685—22no—
106C3×#685C2×C414yescomplemented
107C3×C4×Dic5—22no—
108C3×C4×Dic5—22no—
109Dic3⋊Dic5—22no—
110Dic3⋊Dic5—22no—
111#6667—22no—
112#6667C2×C414yescomplemented
113#6665—22no—
114#6665—22no—
115#6665C2×C414yescomplemented
116Dic3×Dic5—22no—
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119Dic3×Dic5C2×C414yescomplemented
120Dic3×Dic5D414yes—
121C2×C4×#67—51no—
122C2×#885—51no—
123C2×C4×Dic6—51no—
124C3×C4×C22⋊C4—51no—
125C4×#217—51no—
126#4957—51no—
127#4951—51no—
128#4944—51no—
129C4×(C2×D3)⋊C4—51no—
130C4×(C2×D3)⋊C4—51no—
131C42×Dic3—51no—
132#4670—51no—
133#4669—51no—
134#4650—51no—
135#4646D511yescharacteristic, complemented
136C22×C5×Q8—31no—
137C22×D20—31no—
138C22×C4×D5—31no—
139C22×C4×D5C2×D311yescharacteristic
140C2×C5×C4⋊C4—31no—
141C2×C42×C5—31no—
142#4093—38no—
143Q8×Dic5—64no—
144C2×#685—31no—
145C2×#685—31no—
146C2×#685—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#685C2×D311yescharacteristic
153C2×#685C2×D311yescharacteristic
154C2×C4⋊Dic5—31no—
155C2×C4⋊Dic5—31no—
156C2×C4⋊Dic5—31no—
157C2×C4×Dic5—31no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163C2×C4×Dic5C2×D311yescharacteristic
164C2×C4×Dic5C2×D311yescharacteristic
165#4039—64no—
166C5×#95—31no—
167C5×#95—31no—
168C5×#95—31no—
169C5×#95C2×D311yescharacteristic
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963C2×D311yescharacteristic
174C4×#124—151noSylow
175C23×C3×C5C2411yescharacteristic
176C22×D15—21no—
177C22×D15—21no—
178C22×D15—21no—
179C22×D15—21no—
180C22×D15—21no—
181C22×D15—21no—
182C22×D15C22×C412yes—
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C22×C412yes—
198C2×C3×C4×C5#4112yes—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15C22×C412yes—
207C2×Dic15C2×D412yes—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3C22×C412yes—
216C2×C5×Dic3C22×C412yes—
217C2×C5×Dic3C2×D412yes—
218C2×C5×Dic3#4112yes—
219C2×C5×Dic3#4112yes—
220C5×Dic6—28no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5C22×C412yes—
227C2×C3×Dic5C2×D412yes—
228C2×C3×Dic5#4112yes—
229C2×C3×Dic5#4112yes—
230C3×C4×D5—44no—
231#1202—28no—
232#1200—44no—
233C23×C3×C4—51no—
234C22×#67—51no—
235C22×C4×D3—51no—
236C22×Dic6C2×D511yescharacteristic
237C2×C3×C22⋊C4—51no—
238C2×C3×C22⋊C4—51no—
239C2×C3×C42—51no—
240C2×C3×C42—51no—
241C2×#217—51no—
242C2×#217—51no—
243C2×#217—51no—
244C4×#67—104no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—51no—
249C2×(C2×D3)⋊C4—51no—
250C2×C4⋊Dic3—51no—
251C2×Dic3⋊C4—51no—
252C2×Dic3⋊C4—51no—
253C2×Dic3⋊C4C2×D511yescharacteristic
254C2×C4×Dic3—51no—
255C2×C4×Dic3—51no—
256C2×C4×Dic3—51no—
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260C2×C4×Dic3C2×D511yescharacteristic
261#885—58no—
262C4×Dic6—104no—
263C3×#95—51no—
264C3×#95C2×D511yescharacteristic
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95C2×D511yescharacteristic
269C3⋊#95C2×D511yescharacteristic
270C3⋊#95C2×D511yescharacteristic
271C23×D5—31no—
272C23×D5C22×D311yescharacteristic
273C2×C5×Q8—34no—
274C2×C5×Q8—62no—
275C2×C5×Q8—62no—
276C22×C4×C5—31no—
277C22×C4×C5—31no—
278C22×C4×C5—31no—
279C22×C4×C5—31no—
280C22×C4×C5C22×D311yescharacteristic
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C22×Dic5—31no—
284C22×Dic5—31no—
285C22×Dic5—31no—
286C22×Dic5C22×D311yescharacteristic
287C22×Dic5C22×D311yescharacteristic
288C22×Dic5C22×D311yescharacteristic
289C2×D20—34no—
290C2×D20—62no—
291C2×D20—62no—
292C2×C4×D5—22no—
293C2×C4×D5—22no—
294C2×C4×D5—22no—
295C2×C4×D5—62no—
296C2×C4×D5—62no—
297C2×C4×D5—62no—
298C5×C4⋊C4—62no—
299C42×C5—62no—
300#685—22no—
301#685—34no—
302#685—34no—
303#685—34no—
304#685—62no—
305#685—62no—
306#685—62no—
307#685—62no—
308#685—62no—
309#685C4×D314yescomplemented
310C4⋊Dic5—62no—
311C4⋊Dic5—62no—
312C4⋊Dic5—62no—
313C4×Dic5—22no—
314C4×Dic5—22no—
315C4×Dic5—34no—
316C4×Dic5—34no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C4×Dic5—62no—
321C2×#124—151no—
322C2×C4×Q8—151no—
323C2×C4×D4—151no—
324#391—31no—
325#390—151no—
326#388—151no—
327#388—151no—
328#388—151no—
329#388—151no—
330#382—151no—
331C4×C22⋊C4—51no—
332C4×C22⋊C4—151no—
333C4×C22⋊C4—151no—
334C4×C22⋊C4—151no—
335C43—151no—
336C22×C3×C5C23×C411yescharacteristic
337C22×C3×C5C22×D411yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5C2×#4111yescharacteristic
343C2×D15—22no—
344C2×D15—22no—
345C2×D15—22no—
346C2×D15—41no—
347C2×D15—41no—
348C2×D15—41no—
349C2×D15—41no—
350C2×C3×D5—22no—
351C2×C3×D5—22no—
352C2×C3×D5—22no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C3×C4×C5—22no—
358C3×C4×C5—22no—
359C3×C4×C5—41no—
360Dic15—22no—
361Dic15—22no—
362Dic15—41no—
363C3×Dic5—22no—
364C3×Dic5—41no—
365C3×Dic5#12414yescomplemented
366C5×Dic3—22no—
367C5×Dic3—22no—
368C5×Dic3—41no—
369C5×Dic3C4×D414yes—
370C24×C3—51no—
371C23×D3—51no—
372C22×C3×C4—51no—
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4—102no—
376C22×C3×C4—102no—
377C22×C3×C4—102no—
378C22×C3×C4C22×D511yescharacteristic
379C22×C3×C4C22×D511yescharacteristic
380C22×C3×C4C22×D511yescharacteristic
381C2×#67—54no—
382C2×#67—102no—
383C2×#67—102no—
384C22×Dic3—51no—
385C22×Dic3—51no—
386C22×Dic3—51no—
387C22×Dic3C22×D511yescharacteristic
388C22×Dic3C22×D511yescharacteristic
389C22×Dic3C22×D511yescharacteristic
390C22×Dic3C22×D511yescharacteristic
391C2×C4×D3—102no—
392C2×C4×D3—102no—
393C2×C4×D3—102no—
394C2×Dic6—22no—
395C2×Dic6—22no—
396C2×Dic6C4×D514yescomplemented
397C3×C22⋊C4—54no—
398C3×C22⋊C4—102no—
399C3×C42—102no—
400C3×C42—102no—
401#217—54no—
402#217—102no—
403#217—102no—
404(C2×D3)⋊C4—54no—
405(C2×D3)⋊C4—54no—
406(C2×D3)⋊C4—102no—
407(C2×D3)⋊C4—102no—
408(C2×D3)⋊C4—102no—
409C4⋊Dic3—102no—
410Dic3⋊C4—22no—
411Dic3⋊C4—102no—
412Dic3⋊C4—102no—
413C4×Dic3—22no—
414C4×Dic3—54no—
415C4×Dic3—54no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C4×Dic3—102no—
420C23×C5C23×D311yescharacteristic
421C22×D5—21no—
422C22×D5—21no—
423C22×D5—21no—
424C22×D5—21no—
425C22×D5—21no—
426C22×D5—21no—
427C22×D5—32no—
428C22×D5—61no—
429C22×D5—61no—
430C22×D5—61no—
431C22×D5—61no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5C2×C4×D312yes—
435C5×Q8—68no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
445C2×C4×C5—32no—
446C2×C4×C5—32no—
447C2×C4×C5—32no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5—61no—
452C2×C4×C5—61no—
453C2×C4×C5—61no—
454C2×C4×C5—61no—
455C2×C4×C5C2×C4×D312yes—
456C2×C4×C5#23512yes—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—32no—
463C2×Dic5—32no—
464C2×Dic5—61no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5C2×C4×D312yes—
472C2×Dic5#23512yes—
473C2×Dic5D3×D412yes—
474C2×Dic5#23712yes—
475D20—68no—
476C4×D5—44no—
477C4×D5—124no—
478C22×Q8—31no—
479C22×D4—151no—
480C23×C4—51no—
481C23×C4—151no—
482#124—158no—
483C4×Q8—304no—
484C4×D4—304no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—151no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C22⋊C4—51no—
490C2×C22⋊C4—51no—
491C2×C22⋊C4—151no—
492C2×C22⋊C4—151no—
493C2×C22⋊C4—151no—
494C2×C22⋊C4—151no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4—151no—
499C2×C42—31no—
500C2×C42—51no—
501C2×C42—51no—
502C2×C42—151no—
503C2×C42—151no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—151no—
508#95—31no—
509#95—31no—
510#95—31no—
511#95—51no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95D3×D511yescharacteristic
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C4×#4111yescharacteristic
518C2×C3×C5C4×#4111yescharacteristic
519C2×C3×C5C2×#12411yescharacteristic
520C2×C3×C5#52911yescharacteristic
521C2×C3×C5#52911yescharacteristic
522C2×C3×C5#53211yescharacteristic
523D15—42no—
524C3×D5—42no—
525C23×C3—52no—
526C23×C3—101no—
527C23×C3—101no—
528C23×C3—101no—
529C23×C3—101no—
530C23×C3—101no—
531C23×C3—101no—
532C23×C3C23×D511yescharacteristic
533C22×D3—52no—
534C22×D3—101no—
535C22×D3—101no—
536C22×D3—101no—
537C22×D3—101no—
538C22×D3—101no—
539C22×D3—101no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—52no—
548C2×C3×C4—52no—
549C2×C3×C4—52no—
550C2×C3×C4—52no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—204no—
557C2×C3×C4C2×C4×D512yes—
558C2×C3×C4#71312yes—
559#67—108no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—52no—
568C2×Dic3—52no—
569C2×Dic3—101no—
570C2×Dic3—101no—
571C2×Dic3—101no—
572C2×Dic3—101no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3C2×C4×D512yes—
577C2×Dic3C2×C4×D512yes—
578C2×Dic3D4×D512yes—
579C2×Dic3#71112yes—
580C2×Dic3#71312yes—
581C4×D3—204no—
582Dic6—28no—
583C22×C5C22×C4×D311yescharacteristic
584C22×C5C2×#23511yescharacteristic
585C22×C5C2×#23511yescharacteristic
586C22×C5C2×D3×D411yescharacteristic
587C22×C5C2×#23711yescharacteristic
588C22×C5D3×#4111yescharacteristic
589C22×C5D3×#4111yescharacteristic
590C2×D5—22no—
591C2×D5—22no—
592C2×D5—22no—
593C2×D5—41no—
594C2×D5—41no—
595C2×D5—41no—
596C2×D5—41no—
597C2×D5—62no—
598C2×D5—62no—
599C2×D5—62no—
600C2×D5—121no—
601C2×D5—121no—
602C2×D5—121no—
603C2×D5—121no—
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—34no—
607C4×C5—41no—
608C4×C5—62no—
609C4×C5—62no—
610C4×C5—121no—
611Dic5—22no—
612Dic5—41no—
613Dic5—62no—
614Dic5—62no—
615Dic5—121no—
616Dic5#88514yescomplemented
617C24—51no—
618C24—151no—
619C2×Q8—34no—
620C2×Q8—62no—
621C2×Q8—62no—
622C2×D4—154no—
623C2×D4—302no—
624C2×D4—302no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—102no—
633C22×C4—102no—
634C22×C4—102no—
635C22×C4—151no—
636C22×C4—151no—
637C22×C4—151no—
638C22×C4—302no—
639C22×C4—302no—
640C22×C4—302no—
641C22×C4C2×D3×D511yescharacteristic
642C22×C4C2×D3×D511yescharacteristic
643C22×C4C2×D3×D511yescharacteristic
644C4⋊C4—62no—
645C4⋊C4—302no—
646C4⋊C4—302no—
647C4⋊C4—302no—
648C22⋊C4—54no—
649C22⋊C4—102no—
650C22⋊C4—154no—
651C22⋊C4—154no—
652C22⋊C4—154no—
653C22⋊C4—302no—
654C22⋊C4—302no—
655C22⋊C4—302no—
656C22⋊C4—302no—
657C22⋊C4—302no—
658C42—62no—
659C42—102no—
660C42—102no—
661C42—154no—
662C42—154no—
663C42—302no—
664C42—302no—
665C42—302no—
666C42—302no—
667C3×C5C4×#12411yescharacteristic, complemented, Hall
668C22×C3—102no—
669C22×C3—102no—
670C22×C3—102no—
671C22×C3—201no—
672C22×C3—201no—
673C22×C3—201no—
674C22×C3—201no—
675C22×C3C22×C4×D511yescharacteristic
676C22×C3C2×D4×D511yescharacteristic
677C22×C3C2×#71111yescharacteristic
678C22×C3C2×#71311yescharacteristic
679C22×C3C2×#71311yescharacteristic
680C22×C3D5×#4111yescharacteristic
681C22×C3D5×#4111yescharacteristic
682C2×D3—102no—
683C2×D3—102no—
684C2×D3—102no—
685C2×D3—201no—
686C2×D3—201no—
687C2×D3—201no—
688C2×D3—201no—
689C3×C4—22no—
690C3×C4—22no—
691C3×C4—41no—
692C3×C4—54no—
693C3×C4—102no—
694C3×C4—201no—
695Dic3—22no—
696Dic3—22no—
697Dic3—41no—
698Dic3—102no—
699Dic3—102no—
700Dic3—201no—
701Dic3#402714yes—
702C2×C5C4×#23511yescharacteristic
703C2×C5C2×#88511yescharacteristic
704C2×C5#552811yescharacteristic
705C2×C5C4×#23711yescharacteristic
706C2×C5#553811yescharacteristic
707C2×C5C4×D3×D411yescharacteristic
708C2×C5#554811yescharacteristic
709D5—42no—
710D5—122no—
711C23—52no—
712C23—101no—
713C23—101no—
714C23—101no—
715C23—101no—
716C23—101no—
717C23—101no—
718C23—152no—
719C23—301no—
720C23—301no—
721C23—301no—
722C23—301no—
723C23—301no—
724C23—301no—
725C23C22×D3×D511yescharacteristic
726Q8—68no—
727D4—308no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—32no—
740C2×C4—52no—
741C2×C4—52no—
742C2×C4—52no—
743C2×C4—52no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—152no—
757C2×C4—152no—
758C2×C4—204no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—604no—
767C2×C4#677312yes—
768C2×C4C4×D3×D512yes—
769C2×C3—202no—
770C2×C3C2×#402711yescharacteristic
771C2×C3C4×#71311yescharacteristic
772C2×C3C4×#71311yescharacteristic
773C2×C3#6595811yescharacteristic
774C2×C3#6595811yescharacteristic
775C2×C3D5×#12411yescharacteristic
776C2×C3#6605911yescharacteristic
777D3—202no—
778C5C4×#88511yescharacteristic, complemented, Sylow
779C22—102no—
780C22—102no—
781C22—102no—
782C22—201no—
783C22—201no—
784C22—201no—
785C22—201no—
786C22—302no—
787C22—302no—
788C22—302no—
789C22—601no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22C2×#677311yescharacteristic
794C22C2×C4×D3×D511yescharacteristic
795C22D5×#23511yescharacteristic
796C22D3×D4×D511yescharacteristic
797C22D5×#23711yescharacteristic
798C22D3×#71111yescharacteristic
799C22D3×#71311yescharacteristic
800C4—22no—
801C4—22no—
802C4—34no—
803C4—41no—
804C4—54no—
805C4—62no—
806C4—62no—
807C4—102no—
808C4—121no—
809C4—201no—
810C4—302no—
811C4—302no—
812C4—601no—
813C3#1060821111yescharacteristic, complemented, Sylow
814C2—202no—
815C2—602no—
816C2C4×#677311yescharacteristic
817C2#1175310811yescharacteristic
818C2D3×#402711yescharacteristic
819C2D5×#88511yescharacteristic
820C2#1175340011yescharacteristic
821C2#1175348911yescharacteristic
822C2#1175368211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenter#95D3×D5
hypocenterC3×C5C4×#124
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×Dic5×Dic6C2semidirect
4. #11750771C2semidirect
5. C5×#4646C2semidirect
6. C3×#64955C2semidirect
8. #11748875C2semidirect
9. #11748875C2semidirect
10. #11748772C2semidirect
11. #11748710C2semidirect
12. #11748702C2semidirect
13. #11748668C2semidirect
14. #11748652C2semidirect
15. C4×Dic3×Dic5C2semidirect
44. #91455C4semidirect
70. #64955D3semidirect
85. C2×C5×Dic6C2×C4semidirect
100. #6714C2×C4semidirect
106. C3×#685C2×C4semidirect
112. #6667C2×C4semidirect
115. #6665C2×C4semidirect
119. Dic3×Dic5C2×C4semidirect
135. #4646D5semidirect
309. #685C4×D3semidirect
365. C3×Dic5#124semidirect
396. C2×Dic6C4×D5semidirect
616. Dic5#885semidirect
667. C3×C5C4×#124semidirect
778. C5C4×#885semidirect
813. C3#10608211semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#914552
C2×#914442
C2×Dic5×Dic62
#117507712
C5×#46462
C3×#649552
#117489122
#117488752
#117487722
#117487102
#117487022
#117486682
#117486522
C4×Dic3×Dic52
#106082113
C4×#8855